SOLUTION: Given 3 sides of a rectangular fence have a perimeter of 80 feet. Find the largest possible area.

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Question 111370: Given 3 sides of a rectangular fence have a perimeter of 80 feet. Find the largest possible area.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The formula for the perimeter of rectangle is P=2L%2B2W, but since we have 3 sides, the formula becomes P=L%2B2W


Now set the perimeter P equal to 80

80=L%2B2W

Now solve for L

L=80-2W


Now the area of a rectangle is A=L%2AW

A=%2880-2W%29%2AW Plug in L=80-2W


Now plot A=%2880-2W%29%2AW as a function of x. Simply change A to y and w to x to get y=%2880-2x%29%2Ax

+graph%28+500%2C+500%2C+-50%2C+50%2C+-10%2C+800%2C+%2880-2x%29%2Ax%29+

From the graph we can see that the max is at x=20, which means y=800. So when the width is 20 ft the area is maxed out at 800 square feet